Problem: Nadia is 40 years older than William. Seventeen years ago, Nadia was 5 times as old as William. How old is William now?
We can use the given information to write down two equations that describe the ages of Nadia and William. Let Nadia's current age be $n$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $n = w + 40$ Seventeen years ago, Nadia was $n - 17$ years old, and William was $w - 17$ years old. The information in the second sentence can be expressed in the following equation: $n - 17 = 5(w - 17)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to use our first equation for $n$ and substitute it into our second equation. Our first equation is: $n = w + 40$ . Substituting this into our second equation, we get the equation: $(w + 40)$ $-$ $17 = 5(w - 17)$ which combines the information about $w$ from both of our original equations. Simplifying both sides of this equation, we get: $w + 23 = 5 w - 85$ Solving for $w$ , we get: $4 w = 108$ $w = 27$.